Truth value

Have you ever wondered how a computer knows if a statement is correct? It uses something called a truth value. A truth value tells us the relation of a statement to the truth. In classical logic, there are only two possible values. These are true and false. This set of two values is called the Boolean domain.

Scientists often use symbols to show these values. They use the word verum for true. They use the word falsum for false. Truth values help us organize how we think about facts.

Computers use these values to run programs every single day. Many programming languages use a special type called Boolean. In these languages, some expressions are called falsy. This means the computer treats them as false. For example, the number zero is often falsy. An empty list is also often falsy. In the language Lisp, the empty list is called nil.

Other things are called truthy. This means the computer treats them as true. In the language C, any number that is not zero is true. In JavaScript, an empty string is falsy. However, in Python, empty containers like arrays are different.

Math can also use more than just two values. This is called multi-valued logic. Some systems use fuzzy logic to show different degrees of truth. It is not always just on or off. It can be a scale of truth. This might happen on a unit interval.

There is also a type of math called intuitionistic logic. This uses something called a Heyting algebra. In this math, truth values might show where a formula holds. This can involve things like time or location. It is a different way to look at what is valid.

Different rules change how we use these values. In classical logic, we use truth tables to show how things work. We use symbols like conjunction and disjunction. Negation is a rule that swaps true with false.

There are also special rules called De Morgan's laws. These laws show how negation works with other connections. In some advanced math, truth values are seen as sets of programs. This is part of the Curry-Howard correspondence. It shows a link between logic and types. This helps us understand how programs prove things.

Truth values are all around us in the world of ideas. You use them when you decide if a rule is fair. You use them when you sort things into groups. Logic helps us build strong paths for thinking.

Whether it is two values or many, they help us measure truth. They help computers make decisions in a split second. They help mathematicians solve very hard puzzles. Understanding them is like learning the secret language of facts.